Perovskites as ultra-low work function electron emission materials

ABSTRACT

An electron emitter device is provided comprising a cathode comprising a conductive transition metal perovskite oxide comprising mobile conducting electrons exhibiting a conductivity of at least 10−6 Ω−1-cm−1 at room temperature, the transition metal perovskite oxide having a surface from which the mobile electrons are induced to emit upon receiving sufficient energy from an energy source; and an anode electrically coupled to the cathode and positioned to define an interelectrode conductive region between the anode and the cathode, onto which anode the emitted electrons are collected. The transition metal perovskite oxide may have formula Sr1-xBaxVO3. Related methods and devices based on the electron emitter device are also provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional PatentApplication No. 62/278,813 that was filed Jan. 14, 2016, the entirecontent of which is hereby incorporated by reference.

REFERENCE TO GOVERNMENT RIGHTS

This invention was made with government support under FA9550-11-1-0299awarded by the USAF/AFOSR. The government has certain rights in theinvention.

BACKGROUND

Thermionic electron emitters are typically comprised of a refractorymetal such as W coated with an oxide or diffusing oxide species thatlowers the work function via electrostatic surface dipoles. The coatingis necessary because although the refractory metals are stable and goodconductors of electrons, they tend to have high work functions (on theorder of 4.5 eV), and are therefore natively poor electron emittersunless a coating is included to lower their work function. Examples ofthermionic emitters include impregnated W cathodes that have a low workfunction due to the formation of Ba—O dipoles[1] and scandate cathodeswhere a complex interplay between dipole formation and electron dopingof Ba—O on Sc₂O₃ has been proposed to create a low work function.[1-3]These types of thermionic emitters have been employed in many high powerelectron beam applications[4, 5], and even thermionic energy conversionemitting layers rely on the same type of volatile surface dipole layers,such as Cs—O adsorbed on GaAs or InGaAs.[6, 7] However, these emissionmaterials contain volatile surface species, which limits the lifetimeand the efficiency of electronic devices which use thermionic electronemission processes.

SUMMARY

Provided herein are electron emitter devices which comprise transitionmetal perovskite oxides and related methods.

In one aspect, an electron emitter device is provided. In embodiments,an electron emitter device comprises a cathode comprising a conductivetransition metal perovskite oxide comprising mobile conducting electronsexhibiting a conductivity of at least 10⁻⁶ Ω⁻¹-cm⁻¹ at room temperature,the transition metal perovskite oxide having a surface from which themobile electrons are induced to emit upon receiving sufficient energyfrom an energy source; and an anode electrically coupled to the cathodeand positioned to define an interelectrode conductive region between theanode and the cathode, onto which anode the emitted electrons arecollected. The transition metal perovskite oxide does not have theformula (La,Ba,Sr)TiO₃.

In another aspect, a source of microwaves or millimeter waves isprovided, the source comprising the illustrative electron emitterdevice.

In another aspect, a thermionic energy converter is provided, theconverter comprising the illustrative electron emitter device.

In another aspect, a method of generating electrons is provided. Themethod comprises applying energy to the cathode of the illustrativeelectron emitter device, wherein the applied energy is sufficient toinduce the emission of the mobile electrons from the surface of thetransition metal perovskite oxide into the interelectrode conductiveregion, and collecting the emitted electrons on the anode.

Other principal features and advantages of the invention will becomeapparent to those skilled in the art upon review of the followingdrawings, the detailed description, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the invention will hereafter be describedwith reference to the accompanying drawings, wherein like numeralsdenote like elements.

FIGS. 1A-1B show the crystal structures for (FIG. 1A) ideal cubicperovskite and (FIG. 1B) pseudocubic perovskite phases. In both (FIG.1A) and (FIG. 1B) the largest, corner atoms are the A site cations, theatoms at the center of the octahedra are the B site cations, and theother atoms are O. These structures depict high temperature pseudocubicphases that were derived from experimental (FIG. 1A) Pm3m (cubic) and(FIG. 1B) Pbnm (orthorhombic) and R3c (rhombohedral) symmetries. FIGS.1C-1E show structure models of ABO₃ surface slabs (FIG. 1C): asymmetric,stoichiometric, (FIG. 1D): symmetric and AO terminated,nonstoichiometric, and (FIG. 1E): symmetric and BO₂ terminated,nonstoichiometric.

FIG. 2 shows the trend of (001) AO- and BO₂-terminated surface workfunctions for the 18 perovskite materials studied in the Examples as afunction of B-site element across the periodic table. The solid (open)symbols connected with a solid (dashed) line are the BO₂ (AO) workfunctions, respectively. The LaBO₃, SrBO₃, LSM, LaAlO₃ and BSCF seriesof materials are labeled in the figure.

FIGS. 3A-3C show schematic density of states plots for (FIG. 3A)insulating perovskite with empty 3d band such as LaScO₃, (FIG. 3B)perovskite with partially or mostly filled 3d band such as LaNiO₃, and(FIG. 3C) metallic perovskite with minimally filled 3d band such asSrVO₃. The red regions denote O 2p states while the blue regions denoteB 3d states. Shaded regions indicate filled states while unshadedregions denote empty states. The labels and symbols are defined in themain text. The case in plot (FIG. 3C) of a material with minimallyfilled 3d band results in an O 2p-band center furthest below E_(Fermi)and a low work function. The Δ values are defined as the differencebetween the O 2p-band center and E_(Fermi), equivalent to the x-axis ofFIG. 4A-4B.

FIGS. 4A-4B show plots of calculated work functions for the BO₂ (FIG.4A) and AO-terminated surfaces (FIG. 4B) of ABO₃ materials as a functionof the O 2p band center of bulk ABO₃ materials. In both plots, thefilled circles represent insulating perovskites while the open circlesrepresent metallic perovskites. In FIG. 4A there is a semi-quantitativelinear correlation of BO₂ work function with the bulk O 2p-band center.In FIG. 4B there is a semi-quantitative linear correlation for AO workfunction with the bulk O 2p-band center.

FIGS. 5A-5C show SrVO₃ surface slabs of (011) and (111) orientations.FIG. 5A shows the (011) orientation, whereby the top surface isO-terminated and the bottom surface is ABO-terminated. FIG. 5B shows the(111) orientation, with both surfaces terminated as AO₃. FIG. 5C showsthe (111) orientation, now with both surfaces B-terminated. The largespheres are Sr, medium-sized spheres are V (in the middle of theoctahedra), and the small spheres are O.

FIGS. 6A-6C present the results of simulated AO-terminated (001) SrVO₃surfaces with the top SrO layer replaced by varying amounts of A′O(A′=Mg, Ca, Ba) alloying species (A′ doped) with FIG. 6A-6B illustratingthe case for BaO doping. FIG. 6A shows Ba doping in the middle of thesurface slab, resulting in a work function of 1.90 eV. FIG. 6B shows Badoping at the surface of the slab, resulting in an extremely low workfunction of 1.07 eV. The Ba segregation energy was calculated to be−0.64 eV/Ba, and indicates that Ba will preferentially segregate to thesurface. The large light spheres are Sr, the large dark spheres are Ba,medium-sized spheres are V (in the middle of the octahedra), and thesmall spheres are O. The plot in FIG. 6C shows how the calculatedAO-terminated SrVO₃ work function changes when the top surface layer isalloyed with Mg, Ca, and Ba for different concentrations. The onlydopant expected to lower the work function is Ba.

FIG. 7 is a schematic illustration of an electron emitter deviceaccording to an illustrative embodiment.

FIG. 8 is a schematic illustration of a photon-enhanced thermionicenergy converter comprising an electron emitter device according to anillustrative embodiment.

FIG. 9 is a schematic illustration of a traveling wave tube amplifiercomprising an electron emitter device, the amplifier used for millimeterwave and high power radio frequency (RF)/microwave applicationsaccording to an illustrative embodiment.

DETAILED DESCRIPTION

Provided herein are electron emitter devices which comprise transitionmetal perovskite oxides and related methods.

In one aspect, an electron emitter device is provided, comprising acathode comprising a transition metal perovskite oxide and an anodeelectrically coupled to the cathode and positioned to define aninterelectrode conductive region between the anode and the cathode.Electrons are induced to emit from the surface of the transition metalperovskite oxide into the interelectrode conductive region uponreceiving sufficient energy from an energy source, which may be operablycoupled to the cathode. The emitted electrons are collected at theanode. The electron emitter device may comprise an enclosure configuredto enclose the cathode, the anode, and the interelectrode conductiveregion. In some embodiments the enclosed space is evacuated to a vacuum.In alternative embodiments, the enclosed space is filled with anothermaterial, e.g., a solid, a liquid or a gas (or gas mixture). If theenclosed space is filled with a gas or gas mixture, the components ofthe gas and the pressure of the gas may be selected to ensure that theelectron emitter device functions as desired. By way of illustration,the gas components may be selected such that they do not substantiallyalter the surface chemistry of the cathode in order to avoid alteringthe emission properties of the electron emitter device. Similarly, thepressure may be sufficiently low in order to minimize the absorption ordeflection of emitted electrons by the gas components. A variety ofenergy sources may be used. The energy source may be a heat source inwhich case the electrons are emitted via thermionic emission. The energysource may be a voltage source in which case the electrons are emittedvia field emission. The energy source may be a light source (e.g., solarradiation), in which case the electrons are emitted via photoemission.

An illustrative electron emitter device 700 is shown in FIG. 7. Theelectron emitter device 700 comprises a cathode 704 comprising atransition metal perovskite oxide and an anode 708 electrically coupledto the cathode 704 and positioned to define an interelectrode conductiveregion 712. The cathode is operably coupled to an energy source 716 (inthis embodiment, a heater) configured to induce the emission ofelectrons 720 from the surface 724 of the transition metal perovskiteoxide into the interelectrode conductive region 712. An enclosure 728encloses the cathode 704 and the anode 708 such that a vacuum may bemaintained in the space defined by the enclosure 728.

The transition metal perovskite oxide of the cathode may be a compoundhaving Formula I, ABO₃, wherein A and B are cations, typically havingdifferent sizes (i.e., ionic radii). Formula I encompasses doped oralloyed transition metal perovskite oxides, i.e., compounds whichinclude more than one type of A cation (e.g., two, three, etc.) invarying relative amounts (provided the sum of the amounts is about 1atom per a structural A-site), more than one type of B cation (e.g.,two, three, etc.) in varying relative amounts (provided the sum of theamounts is about 1 atom per a structural B-site), or both. By way ofillustration, transition metal perovskite oxides having formula(A₁)_(1-x)(A₂)_(x)(B₁)_(1-y)(B₂)_(y)O₃, wherein x ranges from about 0 toabout 1 and y ranges from about 0 to about 1 are encompassed by FormulaI. With regards to the selection of A₂, A₂ may be a cation which issufficiently electropositive and is present at a sufficient amount toestablish a surface dipole in the transition metal perovskite oxide. Theamount of A₂ may also be selected to provide a sufficient amount of A₂to replenish any A₂ that may be desorbed from the surface of thetransition metal perovskite oxide over time. This amount (and thus x)may be at least about 0.001, at least about 0.01, or at least about 0.1.The selection of A cations (and combinations thereof), B cations (andcombinations thereof) and the relative amounts of the elements toprovide transition metal perovskite oxide compounds exhibiting certaindesirable properties is further described below.

In some embodiments, the transition metal perovskite oxide has FormulaI, wherein A is selected from an alkaline earth element, a rare earthelement, and combinations thereof. In some embodiments, A is selectedfrom an alkaline earth element, a lanthanide, and combinations thereof.In some embodiments, A is selected from Mg, Ca, Sr, Ba, La, Pr, Sc, Y,and combinations thereof. In some embodiments, B is selected from 3dtransition metal elements and combinations thereof. In some embodiments,B is selected from Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and combinationsthereof. In some embodiments, B is selected from 4d transition metalelements such as Nb.

In some embodiments, the transition metal perovskite oxide has FormulaII, AVO₃, wherein A may be as defined above. Formula II also encompassesdoped and alloyed transition metal perovskite oxides having more thanone type of A cation. In some embodiments, the transition metalperovskite oxide has Formula III, (A₁)_(1-x)(A₂)_(x)VO₃, wherein A₁ andA₂ are independently selected from an alkaline earth element and a rareearth element. In some embodiments, A₁ and A₂ are independently selectedfrom Mg, Ca, Sr, Ba, La, Sc, and Y. In some embodiments, the transitionmetal perovskite oxide is Sr_(1-x)Ba_(x)VO₃. As evidenced by theExamples, below, such transition metal perovskite oxides were found toexhibit surprisingly low work functions. This property is surprising, atleast in part, because as compared to other A cations (e.g., La), Srwould be expected to attract electrons, thereby requiring more energy tomove the electron out of the solid material. In addition, based on theresults of the present disclosure, such transition metal perovskiteoxides are expected to exhibit operating lifetime much longer thanconventional dispenser cathode technologies, possibly orders ofmagnitude longer. Another illustrative transition metal perovskite oxideis BaNbO₃.

The formulas above also encompass compounds in which the amounts of theelements may deviate from ideal, e.g., non-stoichiometric compounds. Thedeviation may be up to about 10% in cations (A or B), e.g., up to about6%, up to about 2%, up to about 0.5%, up to about 0.1%, etc. Thedeviation may be up to about 20% in oxygen, e.g., up to about 15%, up toabout 10%, up to about 5%, up to about 1%, up to about 0.5%, etc. By wayof illustration, this means that Formula I, ABO₃, encompasses thecompounds ABO_(2.98), ABO_(2.5), A_(0.95)BO₃, etc.

The formulas above also encompass transition metal perovskite oxidecompounds having different orderings of either the cations, anions, orboth on a perovskite parent lattice, e.g., cubic perovskites, doubleperovskites, which also may be referred to as layered perovskites (wherethe layering refers to planes of ordered ion species in a perovskitelattice), and Brownmillerite phases.

In some embodiments, the transition metal perovskite oxide does not havethe formula (La,Ba,Sr)TiO₃, wherein the relative amounts of La, Ba, Srvary, provided the sum is about 1.

The transition metal perovskite oxide is desirably a compound whichexhibits certain characteristics. As evidenced by the Examples, below, Acations (and combinations thereof) and B cations (and combinationsthereof) may be selected to provide such properties and combinations ofsuch properties. The transition metal perovskite oxide may becharacterized by its work function. In some embodiments, the transitionmetal perovskite oxide exhibits a work function of less than about 2.50eV. This includes embodiments in which the work function is less thanabout 2.20 eV, less than about 2.00 eV, less than about 1.80 eV, lessthan about 1.60 eV, less than about 1.40 eV, less than about 1.20 eV,less than about 1.00 eV, less than about 0.80 eV, or in the range offrom about 0.8 eV to about 2.50 eV. Work function is defined viaEquation 4 below and the work function values above can refer to valueswhich have been calculated as described in the Examples, e.g., usingDensity Functional Theory and at a temperature of 0 K.

The work function of the transition metal perovskite oxide may bemeasured using experimental techniques such as ultraviolet or x-rayphotoemission spectroscopy or Kelvin probe microscopy. The work functionvalues above can refer to values which have been measured experimentallyusing these techniques. Measured work functions may be referred to asthermionic work functions. The work function values above can refer tovalues measured at a temperature range, e.g., about 500° C. to about1500° C., or about 800° C. to about 1000° C. However, since the effectof temperature on work function is on the order of ≈kT (where k isBoltzmann's constant), DFT-calculated, T=0 K work functions provide verygood estimations of the corresponding high temperature thermionic workfunctions.

The transition metal perovskite oxide may be characterized by itsconductivity. In some embodiments, the transition metal perovskite oxideexhibits a conductivity similar to that of graphite or better. In someembodiments, the conductivity is at least about 10⁻¹⁰ Ω⁻¹cm⁻¹ at roomtemperature. This includes embodiments in which the conductivity is atleast about 10⁻⁷ Ω⁻¹cm⁻¹, at least about 10⁻⁴ Ω⁻¹cm⁻¹, at least about10⁻¹ Ω⁻¹cm⁻¹, at least about 10² Ω⁻¹cm⁻¹, at least about 10³ Ω⁻¹cm⁻¹, atleast about 10⁴ Ω⁻¹cm⁻¹, at least about 10⁵ Ω⁻¹cm⁻¹, or in the range offrom about 10⁻⁴ Ω⁻¹cm⁻¹ to about 10⁵ Ω⁻¹cm⁻¹ at room temperature.Transition metal perovskite oxides exhibiting such conductivity areeffective at transporting electrons to the surface from which theelectrons are emitted, which ensures that the material has an amplesupply of near-surface electrons. In addition, such conductivity valuesmay allow the transition metal perovskite oxide to reach a uniformtemperature both within its bulk and on its surface, which is useful forachieving a spatially uniform emission of electrons from the surface.Spatially uniform emission is useful for microwave and millimeter-waveapplications which require a spatially homogeneous beam of electrons tooperate most effectively. The conductivity of the transition metalperovskite oxide may be measured using known four-point probeexperiments which measure conductivity of samples accurately by removingthe contact resistance of the electrodes used in two-point probeexperiments. The conductivity values above can refer to values whichhave been measured experimentally using this technique.

The transition metal perovskite oxide may be characterized by its bandgap. In some embodiments, the transition metal perovskite oxide has aband gap of no more than about 2 eV. This includes embodiments in whichthe band gap is no more than about 1 eV. In some embodiments, thetransition metal perovskite oxide has a band gap of about zero. The bandgap of the transition metal perovskite oxide may be measured usingexperimental techniques such as ultraviolet photoelectron spectroscopy(UPS) or X-ray absorption and emission spectroscopies (XAS, XES). Theband gap values above can refer to values which have been measuredexperimentally using these techniques.

The transition metal perovskite oxide may be characterized by the energydifference Δ between its O 2p-band center and E_(Fermi). The O 2p-bandcenter may be calculated from Equation 1, as described below andE_(Fermi), is the energy of the highest filled electronic state. Asevidenced by the Examples, below, this energy difference Δ was found tostrongly correlate with work function. Transition metal perovskite oxidecompounds having “deep” O 2p-band centers (relative to E_(Fermi)),exhibit lower work functions. In some embodiments, the transition metalperovskite oxide has an energy difference Δ of −3 eV or more (i.e., morenegative). This includes embodiments in which the energy difference Δ is−4 eV or more, −5 eV or more, −6 eV or more, in the range of from about−6 eV to about −3 eV. The energy difference Δ values described above canrefer to a value which is calculated via Equation 1 and DensityFunctional Theory (DFT) calculations using the Heyd, Scuseria, andErnzerhof (HSE) hybrid functionals and a temperature of 0 K as describedin the Examples, below. However, the energy difference Δ values canrefer to a value which is measured experimentally. The position of Ostates relative to the Fermi level can be determined using x-rayabsorption spectroscopy. (See, e.g., Hong, W. T., Shao-Horn, Y., et. al.“Probing LaMO₃ Metal and Oxygen Partial Density of States Using X-rayEmission, Absorption, and Photoelectron Spectroscopy”, Journal ofPhysical Chemistry C, 2015, 119, 2063-2072.) The energy difference Δvalues above can refer to values which have been measured experimentallyusing this technique.

The transition metal perovskite oxide may also be characterized by itschemical stability, including at high temperatures, e.g., up to about500° C. or greater, about 850° C. or greater, about 1000° C. or greater,or about 1500° C. In some embodiments, the transition metal perovskiteoxide is thermodynamically stable at such high temperatures. In someembodiments, the transition metal perovskite oxide may evolve at suchhigh temperatures but is stable for long periods at such hightemperatures.

The surface of the transition metal perovskite oxide from whichelectrons are emitted may be characterized by its crystallographicorientation and termination. In some embodiments, the surface comprisesregions having (001) orientation. In some embodiments, the surfacecomprises regions which are AO-terminated. In some embodiments, thesurface comprises regions having (001) orientation and which are alsoAO-terminated, i.e., regions which have (001) orientation andAO-termination. In some embodiments, the surface may be characterized ashaving substantially (001) orientation and/or being substantiallyAO-terminated. The term “substantially” is used to indicate that theentire surface may not have (001) orientation and/or that the entiresurface may not be AO-terminated, but that enough of the surface adoptsthis orientation and/or termination that it would be considered to havepredominantly (001) orientation and/or AO-termination. In otherembodiments, a sufficient fraction of the surface has (001) orientationand AO-termination such that the surface exhibits a work function whichis substantially similar to (e.g., within ±10%, ±5%, ±2%, ±1%, etc.) thework function of a surface which is substantially (001) orientated andsubstantially AO-terminated. In some embodiments, the fraction of thesurface having (001) orientation and AO-termination is at least about5%, at least about 10%, at least about 25%, at least about 50%. The workfunction of a surface comprising regions having differentcrystallographic orientations and terminations may be referred to as an“effective work function,” since each region will be characterized byits own work function value. However, at high temperatures (e.g., about500° C. to about 1500° C., or about 800° C. to about 1000° C.), electronemission from such a surface will be dominated by the regionscharacterized by relatively low work functions since emission current isexponential with work function.

The form of the transition metal perovskite oxide is not particularlylimited. The cathode may be formed entirely of the transition metalperovskite oxide, which may be shaped into various forms (e.g., plate,wire, tube, etc.) depending upon the application. Such embodiments aredistinguished from those in which the transition metal perovskite oxideis in the form of a layer, coating, or film on the surface of asubstrate. However, in other embodiments, the transition metalperovskite oxide may be in the form of a layer, coating or film on thesurface of a substrate. Various substrates may be used, depending uponthe application. However, as the transition metal perovskite oxideitself can be the material from which the emitted electrons originate(i.e., originating from a conductive band of the transition metalperovskite oxide), the substrate is typically not one which emitselectrons under the particular conditions of the application (althoughit may be). Similarly, as the transition metal perovskite oxide mayexhibit an ultra-low work function, the transition metal perovskiteoxide typically does not require a layer, coating or film of anothermaterial on its surface which further lowers its work function (althoughit may have such a layer).

Methods for making the transition metal perovskite oxides are known.Techniques may include simple mixing and sintering of precursorcompounds; sol-gel deposition; sputtering; thin film growth techniquessuch as molecular beam epitaxy, etc.

The electron emitter devices find use in a variety of applications whichrequire a regular, persistent flow of electrons. Illustrativeapplications include high power electron beam applications such as highpower microwave or millimeter wave source technologies and thermionicenergy conversion devices. An illustrative photon-enhanced thermionicenergy converter comprising an electron emitter device is shown in FIG.8. An illustrative traveling wave tube amplifier used for millimeterwave and high power radio frequency (RF)/microwave applications is shownin FIG. 9. In both figures, the cathodes comprising any of the presenttransition metal perovskite oxides are labeled. In the embodiment ofFIG. 8, the absorption layer is a semiconductor layer, e.g., GaAs,configured to absorb sunlight to generate electrons in the conductionband of the semiconductor. The cathode may also be heated via theelectrical lead. Additional, different, or fewer components than thoseillustrated in the embodiments of FIGS. 8 and 9 may be used.

In another aspect, a method of using the electron emitter devicecomprises applying energy to the cathode of the electron emitter devicesufficient to induce the emission of electrons from the surface of thetransition metal perovskite oxide into the interelectrode conductiveregion, and collecting the emitted electrons on the anode.

EXAMPLES Example 1

Methods

Computational Details:

Calculations were performed using Density Functional Theory (DFT) asimplemented by the Vienna ab initio simulation package (VASP)[8] with aplane wave basis set. The hybrid HSE exchange and correlation functionalof Heyd, Scuseria and Ernzerhof[9] was used with Perdew-Burke-Ernzerhof(PBE)-type pseudopotentials[10] utilizing the projector augmented wave(PAW)[11] method for La, Ca, Mg, Ba, Sr, Sc, Ti, V, Cr, Mn, Fe, Co, Niand O atoms. The fraction of Hartree-Fock (HF) exchange in the HSEmethod for each material was obtained from Refs. [12] and [13]. In Refs.[12] and [13], the fraction of HF exchange was fitted to reproduce theexperimentally-measured bulk band gap and densities of states fromultraviolet photoemission spectroscopy (UPS) measurements. Thus, thefractions of Hartree-Fock exchange used in the HSE calculations were0.25 (LaScO₃), 0.15 (LaTiO₃, LaCrO₃, LaMnO₃, LaFeO₃), 0.125 (LaVO₃),0.05 (LaCoO₃) and 0 (LaNiO₃). For the band insulators SrTiO₃ and LaAlO₃,a value of 0.25 was used for the HF exchange fraction.[14,15] For theremaining materials, the HF exchange values used were the same as therespective transition metal-containing lanthanide perovskite. Therefore,for SrVO₃, SrFeO₃, SrCoO₃, Ba_(0.5)Sr_(0.5)CO_(0.75)Fe_(0.25)O₃ (BSCF)and La_(1-x)Sr_(x)MnO₃ (LSM), the HF values used were 0.125, 0.15, 0.05,0.05 and 0.15, respectively. This method of tuning the amount of HFexchange to reproduce experimental bulk electronic structure propertiessuch as the band gap has been shown to provide more accurate Liinsertion voltages (a quantity that depends sensitively on theelectronic structure near the Fermi level) than the default HF exchangeof 0.25 for a wide range of transition metal oxide materials.[16]

The valence electron configurations of the atoms utilized in thecalculations were La: 5s²5p⁶6s²5d¹, Ca: 3s²3p⁶4s², Mg: 2s²2p⁶3s², Ba:5s²5p⁶6s², Sr: 3s²3p⁶4s², Sc: 3s²3p⁶4s²3d¹, Ti: 3s²3p⁶4s²3d², V:3p⁶4s¹3d⁴, Cr: 3p⁶4s¹3d⁵, Mn: 3p⁶4s²3d⁵, Fe: 3s²3p⁶4s¹3d⁷, Co: 4s¹3d⁸,Ni: 3p⁶4s²3d⁸, Al: 3s²3p¹ and O: 2s²2p⁴ respectively. The plane wavecutoff energies were, at a minimum, 30% larger than the maximum planewave energy of the chosen pseudopotentials, and equal to a minimum of405 eV for all systems. All calculations were performed with spinpolarization. The Monkhorst-Pack scheme was used for reciprocal spaceintegration in the Brillouin Zone for bulk perovskite materials.[17] Forsurface calculations a F-centered reciprocal space integration schemewas used instead of Monkhorst-Pack as only one k-point was used, and theelectronic minimization was performed simultaneously for all energybands. A 2×2×2 k-point mesh was used for the 2×2×2 bulk supercells ofall LaBO₃ materials (40 atoms per cell), with total energy convergence(ionic and electronic degrees of freedom) of 3 meV per formula unit. Forsurface slab calculations, the k-point mesh was reduced to 1×1×1 andmaintained a minimum vacuum distance of 15 Å. It was verified that allcalculated work functions were well-converged (error of approximately+/−0.1 eV) with respect to both slab thickness and vacuum regionthickness, with the exception of LaAlO₃ and LaScO₃, which are highlypolar materials and with work functions which converge very slowly withslab thickness. Therefore, work function results for LaScO₃ and LaAlO₃have a larger error of approximately +/−0.4 eV, based on GGAcalculations of symmetric (001) surface slabs of LaAlO₃ between 5 and 17layers. Lastly, the dipole correction was implemented in VASP to ensurevacuum level convergence, and the dipole correction was calculated onlyin the axial direction normal to the terminating surface.

Perovskite Bulk and Surface Calculations.

In this Example, a total of 18 technologically relevant perovskitematerials were considered: LaBO₃ (B=Sc, Ti, V, Cr, Mn, Fe, Co, Ni),SrBO₃ (B=Ti, V, Fe, Co), La_(1-x)Sr_(x)MnO₃ (x=0.0625, 0.125, 0.25,0.375) (LSM), LaAlO₃ and Ba_(0.5)Sr_(0.5)Co_(0.75)Fe_(0.25)O₃ (BSCF).The specific compositions of LSM and BSCF were included due to the hightechnological relevance of these materials in solid oxide fuel cell andoxygen permeation membrane technology.[18-20] Each of the separate LaBO₃bulk materials were simulated as a pseudocubic 2×2×2 supercell (40atoms, see FIG. 1) while the SrBO₃ bulk materials were simulated with anideal cubic 2×2×2 (40 atoms) supercell. All bulk materials were subjectto a relaxation of volume plus ions, followed by a second relaxation ofions only. However, lattice parameters were kept equal to each other andat right angles to simulate high-temperature cubic or pseudo-cubicstructures, as done by Lee, et. al.[21] All materials which exhibit someform of magnetic ordering were simulated as ferromagnetic, even if theirtrue ground state is not ferromagnetic. For example, LaCrO₃ and LaFeO₃have G-type antiferromagnetic ground states while LaMnO₃ has the A-typeantiferromagnetic ground state. The use of ferromagnetic ordering forall systems is justified. For example, the applications of high powerelectron beams and thermionic energy conversion requireelectron-emitting surfaces maintained at approximately 1000° C. and 500°C., respectively. At these elevated temperatures most perovskitematerials become paramagnetic.[21-23] Ferromagnetic structures thusprovide a consistent and simplified set of magnetic structures toinvestigate the work function trends and physics of these materials. Ithas been found that changing from ferromagnetic to antiferromagnetic forthe cases of LaMnO₃ and LaFeO₃ ordering yielded a calculated workfunction change on the order of 0.1 eV. This change in the work functionwith ferromagnetic versus antiferromagnetic ordering is small comparedto work function differences between different materials, and is notexpected to qualitatively change the trends demonstrated here. It wasassumed that this magnitude of work function difference as a function ofmagnetic ordering is typical for these materials, and thus, everymaterial was modeled with ferromagnetic ordering. The initial bulk 3delectron arrangements for each transition metal in LaBO₃ were, with anominal 3+ oxidation state: Ti: d¹ (t_(2g) ¹), μ_(B)=1, V: d² (t_(2g)²), μ_(B)=2, Cr: d³ (t_(2g) ³), μ_(B)=3, Mn: d⁴ (t_(2g) ³e_(g) ¹),μ_(B)=4 (high spin), Fe: d⁵ (t_(2g) ³e_(g) ²), μ_(B)=5 (high spin), Co:d⁶ (t_(2g) ⁵e_(g) ¹), μ_(B)=2 (intermediate spin), Ni: d⁷ (t_(2g) ⁶e_(g)¹), μ_(B)=1 (low spin). The initial bulk 3d electron arrangements foreach transition metal in SrBO₃ were, with a nominal 4+ oxidation state:Ti: d⁰ (t_(2g) ⁰), μ_(B)=0, V: d¹ (t_(2g) ¹), μ_(B)=1, Fe: d⁴ (t_(2g)³e_(g) ¹), μ_(B)=4 (high spin), Co: d⁵ (t_(2g) ⁴e_(g) ¹), μ_(B)=3(intermediate spin). In all cases, the fully relaxed spin states werevery close to the initial values. LaCoO₃ has been shown to exist indifferent spin states, including low spin,[24] intermediate spin andhigh spin. The usage of the intermediate spin state of Co is justifiedas this state, or some form of spin mixture which might be reasonablyapproximated through intermediate spin, has been shown to exist at roomand higher temperatures.[24-26]

The work function calculations were performed using (001) AO and BO₂terminations for each of the ABO₃ materials. FIG. 1 shows the differentways to create (001) perovskite surface terminations: the surface slabscan be stoichiometric and asymmetric with one surface terminated by AOand one surface terminated by BO₂, or the surface slabs can benon-stoichiometric but symmetric whereby both terminating surfaces areeither AO-terminated or BO₂-terminated. The (001) surface terminationswere used because both experimental and computational work has shownthese surfaces are the most stable surface terminations for manyperovskite systems. References [27] and [28] show via DFT calculationsthat the (001) perovskite terminations are more stable than the (011)and (111) surfaces in the cases of La_(1-x)Sr_(x)Co_(1-y)Fe_(y)O₃ andLaMnO₃, respectively. Recent experimental and computational work by anumber of authors suggest that many transition metal perovskitematerials can be predominantly (001) AO-terminated.[29-34] The fact thatthe AO termination of (001) perovskites tends to be stable is importantfor the present Example as AO-terminated perovskite surfaces exhibitmuch lower work functions than BO₂-terminated surfaces (see “ABO₃calculated work functions”). In the present Example, all surface slabs(except La_(1-x)Sr_(x)MnO₃) were simulated with 9 layers that wereeither AO- (88 atoms per supercell) or BO₂- (92 atoms per supercell)terminated. The top two atomic layers of each surface were allowed torelax while the remainder of the surface slab was frozen to be bulk-likeABO₃. For the calculations of La_(1-x)Sr_(x)MnO₃ surfaces, 8-layerasymmetric slabs were used in order to maintain the same Srconcentration for calculations of the AO and BO₂ work functions, sinceif symmetric slabs were used then the total number of A-site atoms wouldchange when considering the symmetric AO termination versus thesymmetric BO₂ termination. The placement of Sr within theLa_(1-x)Sr_(x)MnO₃ surface slabs was performed as follows. For Srconcentrations of x=0.0625, 0.125, and 0.25, one Sr was placed on theAO-terminated surface (surface concentration of 25% A-site fraction)while the remaining Sr were ordered through the AO planes of thesimulation cell such that all Sr were as far as possible from eachother. For Sr content of x=0.375, the x=0.25 structure was used with theadditional Sr placed on the terminating surface in order to reflect thetendency of Sr segregation to the surface in this material.[35,36] Itwas verified for a single Sr concentration of x=⅛ that increasing theslab thickness from 8 to 12 layers resulted in a work function change ofless than 0.05 eV, indicating satisfactory convergence. Therefore,reported work functions for La_(1-x)Sr_(x)MnO₃ surfaces using 8 layerslabs should be sufficiently accurate.[35]

From the standpoint of formal valences, all LaBO₃ materials areconsidered part of the “3-3” perovskites, meaning that both cationsadopt a nominally 3+ oxidation state, while O has its typical 2−oxidation state. When the A-site contains Sr in place of La, Sr adopts a2+ oxidation state and the B-site cation oxidizes from 3+ to 4+, so forexample SrCoO₃ and BSCF materials are “2-4” perovskites. For 3-3perovskites, each AO layer is nominally 1+ while each BO₂ layer isnominally 1−. The stoichiometric, asymmetric termination shown in FIG. 1has ionic layers that alternate +/−/+/−, with a positively charged AOtermination on one side and a negatively charged BO₂ termination on theother. This creates an energy that diverges with slab thickness unlessthe dipole is screened, and has been termed the polarcatastrophe.[37,38] For surface slabs simulated using DFT, this surfacegeometry creates a very large surface dipole that, in the calculations,must be compensated by a movement of charge across the surface slab,i.e. an electronic reconstruction. This electronic reconstruction tendsto create large changes in the electronic structure of the material, forexample highly polar perovskites will move large amounts of charge tocompensate the large surface dipole which can lead to surfacemetallization in insulators.[35] By contrast, the symmetric slabs shownin FIG. 1 which are terminated either with both surfaces as AO or bothsurfaces as BO₂ will not exhibit the large surface dipole, and aperovskite which shows bulk insulating properties will retain itsinsulating nature in the surface slab. These symmetric surface slabs areoff-stoichiometric, therefore an electron excess (deficiency) willresult for the AO- (BO₂-) terminated systems. Therefore, the symmetricAO-terminated system represents the n-type (low work function) limitwhile the symmetric BO₂-terminated system represents the p-type (highwork function) limit for each material. Therefore, it is expected in thecase of experimentally measured pure systems that the observed workfunctions may vary between values reported here for the n-type(AO-terminated) and p-type (BO₂-terminated) limits. For perovskiteswhich have a band gap, it is also possible to further tune the value ofthe work function by doping extrinsic elements to move the Fermi levelto a more p-type (higher work function)[39] or n-type (lower workfunction) value. However, one should not generally expect that a shiftin Fermi level by bulk doping of an insulator will result in an equalcorresponding change in the work function. This lack of simplecorrelation may be the result of interactions between the bulk dopantsand surface dipoles, which yield a more complex cumulative effect ofbulk Fermi level and surface dipole changes on the work function.[2] Forthe 3-3 perovskites it is expected that the symmetric slabs are morephysically representative of (001) perovskite films in the thick filmlimit (where the terminating surfaces are independent of each other)because the polarity is completely compensated.[35] For materials thatcan easily move electrons to compensate the surface polarity (e.g.LaMnO₃, LaNiO₃), one can use thinner slabs such as an 8 layer asymmetricslab and obtain the same answer for the calculated work function (i.e.the work function converges quickly with increasing slab thickness). Formaterials that are very insulating such as LaScO₃ and LaAlO₃, movementof electrons to compensate the polarity of the asymmetric slab isdifficult and convergence of the work function with slab thicknessrequires many layers, in some cases dozens.[35]

In “O 2p-band center as an electronic structure descriptor” the O2p-band center Ō_(2p)(E) is used. Ō_(2p)(E) is the centroid of theelectronic density of states projected onto the O 2p orbitals referencedto an energy level (here the Fermi energy E_(Fermi) is used) and wascalculated as:

$\begin{matrix}{{{{\overset{\_}{O}}_{2p}(E)} = {\frac{\int_{- \infty}^{\infty}{{E \cdot {D_{O_{2p}}(E)}}{dE}}}{\int_{- \infty}^{\infty}{{D_{O_{2p}}(E)}{dE}}} - E_{Fermi}}},} & {{Equation}\mspace{14mu}(1)}\end{matrix}$where

D_(O_(2p))(E) is the density of states projected onto the O 2p orbitals. In Eq.(1), the integrals were taken over all electronic states. The numeratoris also called the first moment of the projected density of states, andthe denominator is the integral over the projected density of states,yielding the electron occupation for the 2p orbitals of oxygen. In allcases, the bulk ABO₃ materials were used for the O 2p band centercalculations, and this point will be stressed in the followingdiscussion.

In “SrVO₃ as a low work function, metallic perovskite” additionalsurface terminations of SrVO₃ were examined. Therefore, it becomesimportant to ascertain which crystallographic surface termination is themost stable one, as an experimentally measured effective work functiondepends on the proportion of each surface termination present. Thesurface energy is defined as the formation energy to create a specificsurface termination from the equivalent amount of bulk material, and isnormalized by the surface area. For a stoichiometric slab such as (011)terminations, the surface energy γ is calculated as:

$\begin{matrix}{{\gamma = {\frac{1}{2A}\left( {E_{x,{surface}} - {xE}_{bulk}} \right)}},} & {{Equation}\mspace{14mu}(2)}\end{matrix}$where A is the surface area, E_(x,surf) is the total energy of a surfaceslab containing x formula units, and E_(bulk) is the total energy of asingle formula unit in the bulk form. The quantity in the parenthesisrepresents the energy difference between the equivalent amount ofmaterial in a surface slab versus bulk form. The factor of 2 is presentbecause the slab contains two surfaces. For the (001) and (111)symmetric slab calculations, the surface slabs are off-stoichiometric.Therefore, the energies of the two slab terminations (e.g. AO (001) andBO₂ (001)) must be added together and the resultant surface energy isthus an average of the two surface terminations:

$\begin{matrix}{{\gamma = {\frac{1}{4A}\left( {\left( {E_{x,{{surface}\; 1}} + E_{y,{{surface}\; 2}}} \right) - {\left( {x + y} \right)E_{bulk}}} \right)}},} & {{Equation}\mspace{14mu}(3)}\end{matrix}$

where E_(x,surface1) is the total energy of the first surfacetermination containing x formula units, E_(y,surface2) is the totalenergy of termination 2 containing y formula units, and the factor of 4is present because the addition of two separate slab calculations meansthere are actually four surfaces being formed instead of two.

Calculating the Work Function.

The work function Φ of a material is the energy required to pull anelectron from the Fermi level E_(Fermi) (electron chemical potential) tothe vacuum level E_(vac):Φ=E _(vac) −E _(Fermi).  Equation (4)E_(vac) is the energy level at which the electron has zero kineticenergy at a semi-infinite distance away from the surface and the imagecharge restoring force on it can be considered negligible. The workfunction can be measured using experimental techniques such asultraviolet or x-ray photoemission spectroscopy, Kelvin probemicroscopy, and calculated with Density Functional Theory (DFT). UsingDFT, the work function of any surface can be determined by calculatingthe electrostatic potential energy, identifying E_(vac), calculatingE_(Fermi), and subtracting E_(Fermi) from E_(vac).

Introduction

Knowledge of work function values of different crystallographicorientations and terminations is valuable for engineering specificsurface and interfacial properties for applications including chargeinjection layers, electrocatalysts, and thermionic electron or fieldemission-based high power devices. A detailed analysis of the physicsgoverning the work functions of perovskite oxides has not beenpreviously established. In this Example, the work function trends of aseries of perovskite (ABO₃ formula) materials were examined usingDensity Functional Theory. The results show that the work functions of(001)-terminated AO- and BO₂-oriented surfaces can be described usingconcepts of electronic band filling, bond hybridization, and surfacedipoles. An approximately linear correlation between perovskite workfunctions and the bulk oxygen band center was found. This correlationwith oxygen band center enables both understanding and rapid predictionof trends in work function. Finally, SrVO₃ was identified as a stable,low work function, highly conductive material for a new electronemission cathode for application in high power beam devices and as apotential electron emissive material for thermionic energy conversiontechnologies.

Results and Discussion

High temperature 2×2×2 pseudocubic structures adopted from ideal cubicABO₃ perovskite (Pm3m, SrTiO₃, SrVO₃, SrFeO₃, SrCoO₃,Ba_(0.5)Sr_(0.5)Co_(0.75)Fe_(0.25)O₃), orthorhombic perovskite (Pbnm,LaScO₃, LaTiO₃, LaVO₃, LaCrO₃, LaMnO₃, La_(1-x)Sr_(x)MnO₃, LaFeO₃), andrhombohedral perovskite (R3c, LaCoO₃, LaNiO₃) examined in this study areshown in FIGS. 1A-1B. FIG. 1C shows the asymmetric (used forLa_(1-x)Sr_(x)MnO₃) and FIGS. 1D-1E shows the symmetric (used for allother materials) surface slabs used for the work function calculations.

ABO₃ Calculated Work Functions.

FIG. 2 is a plot of the calculated work functions for the AO- andBO₂-surface terminations versus composition of the B-site element forall 18 materials considered. Since the B-site element changes from Scthrough Ni, FIG. 2 is a plot of how the AO and BO₂ work functions forperovskite materials change as B-site cations move across the 3d seriesof the periodic table. Table 1 contains the calculated work functionsfor the AO- and BO₂-terminated (001) surfaces for all ABO₃ materialsconsidered in this Example. The O-bond ionicities are also provided, andwere calculated using Bader charge analysis of atomic charges of bulkABO₃ materials.[40,41] An O-bond ionicity equal to 1 indicates that thecharge state of the O atoms in the ABO₃ material is −2, i.e. that theO-bond is completely ionic. Generally, chemical bonding has mixedcovalent and ionic character, therefore the calculated atomic chargesfrom the Bader analysis will be less than −2 (for example, an O atomiccharge of −1.5 yields a bond ionicity of −1.5/−2=0.75). The O-bondionicities in Table 1 will be referenced in upcoming qualitativediscussions of work function trends for these materials. For the LaBO₃series, the LaO work functions range between 1.76 eV (LaMnO₃) to 3.57 eV(LaScO₃) while the BO₂ work functions range from 2.72 eV (LaTiO₃) to6.87 eV (LaAlO₃), and tend to increase in magnitude for Ti through Ni.For the SrBO₃ series, the SrO work functions range between roughly 1.86eV (SrVO₃) to 3.42 eV (SrCoO₃) while the BO₂ work functions range from5.09 eV (SrVO₃) to 6.68 eV (SrFeO₃).

TABLE 1 Summary of HSE calculated work functions for all (001) surfacesof ABO₃ materials considered in this Example. Also listed are theionicities of the O-bonds for each material, which were calculated fromBader charge analysis of the bulk materials. A decrease in bondingionicity is indicative of greater hybridization of the B 3d bands and O2p bands. AO BO₂ O bond Material WF(eV) WF(eV) ionicity LaScO₃ 3.57 6.320.716 LaTiO₃ 2.59 2.99 0.684 LaVO₃ 2.97 3.60 0.664 LaCrO₃ 2.77 5.270.665 LaMnO₃ 1.76 5.21 0.653 LaFeO₃ 1.98 5.14 0.637 LaCoO₃ 2.42 5.730.599 LaNiO₃ 2.47 6.06 0.559 LaAlO₃ 3.25 6.87 0.879 SrTiO₃ 3.18 6.330.655 SrVO₃ 1.86 5.09 0.601 SrFeO₃ 3.24 6.68 0.556 SrCoO₃ 3.42 6.510.537 Ba_(0.5)Sr_(0.5)Co_(0.75)Fe_(0.25)O₃ 2.94 6.35 0.540La_(0.9375)Sr_(0.0625)MnO₃ 2.11 5.28 0.650 La_(0.875)Sr_(0.125)MnO₃ 2.235.49 0.647 La_(0.75)Sr_(0.25)MnO₃ 1.87 6.02 0.643La_(0.625)Sr_(0.375)MnO₃ 2.39 5.85 0.637

Perhaps the most striking feature of the work functions is that the AOsurfaces have lower work function values than BO₂ surfaces in all cases.Qualitatively, this can be understood in terms of the surface dipoles.The alternating layers of the (001) orientation are AO/BO₂/AO/BO₂,which, when considering formal charges, alternates +/−/+/−. A positivesurface dipole is a dipole with an outwardly pointing positive charge,while a negative surface dipole has an outwardly pointing negativecharge. Thus it is seen that the AO termination forms a positive surfacedipole that lowers the work function, and the BO₂ surface forms anegative surface dipole that increases the work function.

The trend of increasing BO₂ work function when proceeding from left toright on the periodic table along the 3d row can be understood from thestandpoint of transition metal electronegativities. When proceeding fromTi to Ni, the electronegativity of the transition metal ion isincreasing as the 3d band fills. As a result, the 3d bands shift lowerin energy as they fill and the work function increases. For thematerials LaScO₃, LaAlO₃ and SrTiO₃, the 3d bands are nearly empty andthese materials behave as band insulators. Interestingly, thesematerials have nearly the same BO₂ and AO work function values within afew tenths of an eV. This suggests that, in the absence of 3d electrons,it is the O 2p band that is effectively setting the value of the workfunction. This trend will be discussed in more detail in “Work functiontrends: band perspective” and “O 2p-band center as an electronicstructure descriptor.”

From Table 1, it is evident that as the 3d band fills, the bondingionicity decreases. This trend is equivalent to saying that the B 3d andO 2p bands are becoming more hybridized. In addition, for the SrBO₃materials where the B element is in the 4+ oxidation state, the bondionicities are lower and thus the B 3d and O 2p bands are morehybridized than the analogous LaBO₃ systems where the B element is inthe 3+ oxidation state. These trends of B 3d-O 2p band hybridization areconsistent with a joint experimental and computational work by Suntivichand coworkers that showed how B 3d− O 2p band hybridization changes as afunction of 3d band filling using O K-edge x-ray absorption and DFTcalculations on a series of perovskite and Ruddlesden-Poppermaterials.[42] The increased B 3d−O 2p band hybridization means there isgreater overlap of the B 3d and O 2p bands, and the O 2p band becomescloser to E_(Fermi). Therefore, these trends illustrate that materialswith greater band hybridization will have higher BO₂ work functions andO 2p bands that are closer to E_(Fermi). Both of these points will beexpanded upon in “Work function trends: band perspective” and “O 2p-bandcenter as an electronic structure descriptor.”

Interestingly, the trend of increasing BO₂ work function with increasedfilling of the B 3d band is not present for the AO work function. The AOwork function trend is approximately flat with values of approximately2-3 eV regardless of the B-site element. A fixed AO surface would beexpected to have a work function that follows the trends set by thechanging 3d band levels, just as the BO₂ surface appears to do. Instead,the expected trends of AO work function values are suppressed almostentirely by differences in the AO surface dipole between thesematerials. The difference in the surface dipole between the AO and BO₂surfaces is simply proportional to the difference in their workfunctions ΔΦ through the Helmholtz equation, which has the form

${{\Delta\;\Phi}\; = {\frac{- e}{ɛ_{0}A}{{\overset{\rightarrow}{p}}_{z}}}},$where e is electronic charge, ε₀ is the vacuum permittivity, A issurface area and |{right arrow over (p)}_(z)| is the dipole magnitudenormal to the surface. However, since the BO₂ surface work function ischanging as expected with the bulk Fermi level and band filling whilethe AO work function is not, it can be said with confidence that the BO₂surface dipole is relatively constant while it is the AO surface whosedipoles are changing with the B-site cations.

The constant dipole on the BO₂ surface can be understood by inspectingthe densities of states of these materials and from the schematic bandstructures shown in FIGS. 3A-3C. These densities of states show that formaterials containing 3d electrons the states at E_(Fermi) are dominatedby B 3d with O 2p states. Furthermore, the O 2p band remains largelyfixed in energy. A possible reason that BO₂ surfaces exhibit a nearlyconstant surface dipole is because the electrons at E_(Fermi) arealready at the terminating surface, and don't have to pass through anadditional AO layer as they are emitted into vacuum. In this way,emission from the BO₂ surface may be the result of E_(Fermi) beingpinned at the surface by the B 3d states, and is thus dominated by the B3d band filling and E_(Fermi) position, while emission from the AOsurface can be thought of as taking an electron from E_(Fermi), which iscomprised of mostly mixed B 3d and O 2p states in the BO₂ layer, andmoving it through the positively-oriented AO surface dipole layer toemit into vacuum.

Doping Sr into LaMnO₃ to produce LSM resulted in an increase of the AOand BO₂ work functions for all Sr concentrations, however the increasein the work function is not monotonic with increasing Sr content. Thislack of monotonic behavior is most likely a result of the specific Srordering chosen. When replacing La³⁺ with Sr²⁺, the system becomes moreoxidized, i.e. it becomes hole-doped. This is evident from the workfunction data for the LSM series, where increasing the A-site Sr contenttends to increase the work function of both surfaces and decrease theionicity of the O-bonding. The fact that all BO₂ and most AO SrBO₃material work functions are higher than their corresponding LaBO₃ workfunctions (with the exception of AO-terminated SrVO₃) demonstrates thatdoping Sr in place of La should raise the work function of theperovskite. Interestingly, BSCF has a lower work function than bothSrFeO₃ and SrCoO₃, suggesting that doping Ba in place of Sr results in alowering of the work function for Sr-based perovskites. The effect of Badoping on the SrVO₃ work functions will be examined further in “SrVO₃ asa low work function, metallic perovskite.”. The AO-terminations ofSrVO₃, LaMnO₃ and LaFeO₃ have the lowest calculated work functions of1.86 eV and 1.76 eV, and 1.98 eV respectively, making them desirable forlow-work-function, electron-emission cathode materials. Of thesematerials, SrVO₃ also offers metallic conductivity, ability to besynthesized as both a bulk powder[43,44] and (001)-oriented thinfilm,[45] and structural stability at high temperatures.[43,44,46] SrVO₃is studied in more detail in “SrVO₃ as a low work function, metallicperovskite.”

Work Function Trends: Band Perspective.

FIGS. 3A-3C is a density of states schematic that illustrates the trendof BO₂ work functions from FIG. 2 by comparing the density of states ofan insulating material with an empty 3d band and high ionicity (smallamount of B 3d− O 2p hybridization) such as LaScO₃ (FIG. 3A), a lessionic material (large amount of B 3d− O 2p hybridization) with half ormostly filled 3d band such as LaNiO₃ (FIG. 3B) and a metallic, mediumionicity material (medium amount of B 3d− O 2p hybridization) with aminimally occupied 3d band such as SrVO₃ (FIG. 3C). The vacuum level,Fermi level and O 2p-band center are denoted as E_(vac), E_(Fermi), andŌ_(2p)(E), respectively. The position of E_(Fermi) is at the energy ofthe highest filled electronic state. The O 2p states are shown in redand the B 3d states are shown in blue. The states that are shaded arefilled states. In FIGS. 3A-3C, the approximation was made that the O 2pbands remain at a fixed energy level. While this is not rigorously true,the O 2p bands move only a few tenths of an eV in energy relative to thevacuum level, which is small compared to the multiple eV energy changeof the B 3d bands as a function of the B-site composition. Maintaining aconstant level of the O 2p band provides a more straightforward andintuitive way to demonstrate how the work function varies with bondionicity/hybridization and also how the value of the O 2p band center(x-axis in FIG. 4) physically relates to the calculated work functionvalues. The Δ values indicate the energy difference between the O2p-band center and E_(Fermi), equivalent to the x-axis of FIG. 4. InFIG. 3A, the insulating perovskite with empty 3d band has very deep O 2pbands which results in a deep E_(Fermi), an O 2p-band center close toE_(Fermi) and high work function. In FIG. 3B, the perovskite withpartially filled 3d band has a large amount of O 2p-metal 3d bandhybridization (i.e. lower ionicity/higher covalency) which results inhigher occupied electron energy states, an O 2p-band center further fromE_(Fermi) compared to FIG. 3A, and a slightly lower work function. InFIG. 3C, the metallic perovskite with minimally filled 3d band has lessO 2p− metal 3d band hybridization than the case in FIG. 3B, whichresults in an occupied portion of the B 3d band that is more empty, lesshybridized and is higher in energy. Since the occupied portion of the B3d band is higher in energy, E_(Fermi) is also higher. Overall, thisleads to an O 2p-band center that is further from E_(Fermi) and a lowerwork function.

O 2p-Band Center as an Electronic Structure Descriptor.

Having demonstrated qualitative work function trends with changing A-and B-site composition for the ABO₃ materials investigated here, thefocus was turned to developing a greater understanding of the physicsgoverning the value of the work function in these perovskite materials.To accomplish this, the O 2p-band center was used as an electronicstructure descriptor, as this variable has proved useful for correlatingwith a number of perovskite properties.[25,47-49] The B-site cation3d-band center and the La/Sr A-site band centers (both calculated withrespect to E_(Fermi)) were also investigated as possible descriptors.However, no useful physical trends emerged from those analyses.

FIGS. 4A-4B demonstrate the relationship between the calculated (001)work functions and the value of the bulk O 2p-band center. FIG. 4A (FIG.4B) is a plot of BO₂ work function (AO work function) as a function ofthe O 2p-band center energy. In both plots, the filled circles refer toinsulating perovskites while open circles refer to metallic perovskites.In the present case, “insulating” refers to any material calculated tohave a finite bulk and surface band gap, whether due to band-insulatingor Mott-Hubbard insulating behavior. The materials which compose the setof insulating perovskites are: LaScO₃, LaTiO₃, LaVO₃, LaCrO₃, SrTiO₃ andLaAlO₃. The twelve remaining perovskite materials are referred to as“metallic” perovskites. Although the bulk ground states of some of thesematerials, for example LaMnO₃ and LaFeO₃, are also insulating in aformal sense, the ferromagnetic near-surface electronic structure ismetallic.[35] Therefore, the inclusion of LaMnO₃ and LaFeO₃ in thecategory of “metallic” perovskites is not arbitrary, as these materialsdemonstrate fundamentally different electronic structure behavior thanprototypical Mott-Hubbard insulators such as LaTiO₃ and LaVO₃ near thesurface.

Both plots of FIGS. 4A-4B show a linear trend of the calculated workfunction versus the bulk O 2p band center, although the trend is moreconsistently linear in the case of BO₂ work functions. In general, theseresults demonstrate that the bulk O 2p band center provides anapproximate quantitative predictor of the work function. Interestingly,in FIG. 4A, the slope of the BO₂ work function versus O 2p band centeris approximately 1, while in FIG. 4B the slope of the AO work functionis approximately 0.25-0.5. This result demonstrates that the BO₂ workfunction change is dominated by the energy difference between the O 2pband center and E_(Fermi), which is changing as a result of the fillingof the B 3d bands with B-site composition. This result thereforedemonstrates that the surface dipole effects are largely constant indetermining the BO₂ work function. In the case of the AO work functions,where the work function doesn't change in direct proportion to themovement of the O 2p band center, changing surface dipoles clearly playa much larger role in determining the work function.

From the above discussions the understanding of the trend in O 2p bandwith the work function may be summarized as follows: The location of theO 2p band is, within a few tenths of an eV, fixed relative to the vacuumlevel, and its energy relative to E_(Fermi) is highly dependent on thenumber of 3d electrons in the system and the bond hybridization(ionicity) between the B 3d levels and O 2p levels. When proceeding fromTi through Ni and adding more 3d electrons to the system, the bondhybridization increases, the 3d bands fill and move lower in energy, andthus E_(Fermi) is lower in energy and closer to the (approximately fixedrelative to vacuum) O 2p band center. Since E_(Fermi) is lower inenergy, the work function of BO₂ surfaces increases as more 3d electronsare added. Furthermore, for the same B-site transition metal element, ifthe B-site is more oxidized (e.g. comparing Co³⁺ in LaCoO₃ with Co⁴⁺ inSrCoO₃), the material containing the more oxidized transition metal willexhibit greater hybridization between the B 3d and O 2p bands, thusresulting in higher work functions. From Table 1 and FIG. 2, it can beseen that all SrBO₃ materials have higher work functions than theiranalogous LaBO₃ materials, except for AO-terminated SrVO₃. Thesehybridization trends with 3d electron filling are consistent withexperimental and computational findings of Suntivich and coworkers.[42]Broadly, the band structure progression shown in FIGS. 3A-3C is a closerepresentation of how the BO₂ work function changes with composition and3d band filling. In the case of the AO work function, the physics ofFIGS. 3A-3C certainly plays a role, but as the slopes of work functionversus O 2p band center in FIG. 4B are not close to one, the remainingportion of the work function change is due to surface dipoles, asdiscussed in “ABO₃ calculated work functions.”

SrVO₃ as a Low Work Function, Metallic Perovskite.

The earlier analysis in “Work function trends: band perspective” hasdemonstrated that of the 18 perovskite materials considered here, SrVO₃has an extremely low work function, rendering it particularly useful forelectron emitting applications, e.g., for high power electron beamdevices used in defense, scientific research and communications and asan electron-emitting layer in the renewable energy technology ofphoton-enhanced thermionic energy conversion devices. The metallicperovskite SrVO₃ has been successfully synthesized both as a bulkpolycrystalline powder[43,44] and as a controlled (001)-oriented thinfilm grown with MBE.[45] SrVO₃ possesses a very high conductivity ofabout 10⁵ Ω⁻¹cm⁻¹ at room temperature, higher than SrRuO₃ (aprototypical metallic perovskite) and on par with elemental metals suchas Pt.[45] SrVO₃ maintains its structural stability even up to hightemperatures of 1300° C. and under reducing conditions during annealingwith an H₂/N₂ or H₂/Ar gas atmosphere.[43,44,46] Moreover, there areopportunities with doping SrVO₃ to lower its work function further. Inthis section, alkaline earth metal doping in SrVO₃ is considered. Alsoconsidered are the pristine (011) and (111) surface terminations toascertain the full work function range of SrVO₃ and also obtain a morequantitative understanding of which surface terminations should bestable (and thus present in the highest quantity) in a real device. Inaddition, the effect of surface segregation in SrVO₃ is considered.

FIGS. 5A-5C illustrates the surface structures of (011) and (111)terminated SrVO₃. From FIG. 5A, the (011) termination can either beO-terminated or ABO-terminated. FIGS. 5B and 5C show symmetric (111)surfaces that are B-terminated (FIG. 5B) and AO₃-terminated (FIG. 5C).The work functions and surface energies for these surface terminations(as well as surface energies for (001) surfaces) were calculated and aretabulated below in Table 2.

TABLE 2 Tabulated values of calculated work functions and surfaceenergies for different SrVO₃ surface terminations. The work functions of(001) surfaces are repeated from Table 1 for clarity. Termination WorkFunction (eV) Surface Energy (eV/Å²) (001) 1.86 (AO), 5.09 (BO₂) 0.052(AO/BO₂ average) (011) 2.32 (ABO), 7.23 (O) 0.094 (O/ABO average) (111)2.78 (B), 4.68 (AO₃) 0.078 (B/AO₃ average)

From Table 2, it can be seen that the pristine (001) surfaces have alower surface energy and thus are more stable than (011) and (111)surfaces, consistent with previous DFT studies.[27,28] Recentexperimental LEIS measurements show that numerous perovskite materialshave dominant (001) surface terminations that are most likelyAO-terminated.[29,30,50] From the current calculations, overall order ofstability is: γ(001)<γ(111)<γ(011). The ABO-terminated (011) surface hasa reasonably low work function of 2.32 eV, but overall the (011) and(111) surfaces possess higher work functions than AO-terminated (001).The fact that the (001) terminations of SrVO₃ are predicted to be thestable terminations, together with the fact that AO-terminated (001)SrVO₃ exhibits the lowest work function of the surfaces explored herefurther reinforces SrVO₃ as a new low work function material.

Next, the effect of doping the alkaline earth metals Mg, Ca and Ba inSrVO₃ was examined. From FIG. 2, it was suggested from comparing thework function values of SrFeO₃, SrCoO₃, and BSCF that doping Ba onto theA-site of Sr-based perovskites may result in a lowering of the workfunction. Here, the focus is solely on the AO-terminated (001) surfaceof SrVO₃ since this is the low work function surface termination ofinterest. The AO-terminated (001) surface was simulated withconcentrations of 25%, 50% and 100% site fraction Mg, Ca and Ba(equivalent to replacing one SrO row with a (Mg, Ca, Ba)O row) on thesurface of the AO (001) slab (see FIG. 6C). It was found that surfacedoping of Mg and Ca raised the work function for all concentrations,while doping Ba lowered the work function for all concentrations. Inparticular, a site fraction of 100% Ba on the surface resulted in a verylow work function of just 1.07 eV.

To better understand the role of Ba doping in lowering the work function(i.e. bulk doping versus surface dipole formation), also simulated was afull layer of BaO in place of SrO in the middle of the AO (001) slab. Itwas found that placement of Ba in the middle of the slab resulted in abarely increased work function of 1.90 eV, which is 0.04 eV higher thanpure SrVO₃. However, placement of the Ba in the top surface layerresulted in a profound lowering of the work function down to 1.07 eV,which is 0.79 eV lower than pure SrVO₃. This indicates that the workfunction lowering from Ba doping is due entirely to altering the surfacedipole. By comparing the atomic positions of a pristine SrVO₃ surfaceand SrVO₃ with Ba in the surface layer, it is clear that the bondlengths between Ba and sub-surface O (the O in the BO₂ layer beneath thesurface) is about 0.2 Å longer than the bond length between Sr and thesame sub-surface O. This longer bond length is most likely the result ofthe larger ionic radius of Ba (1.75 Å) over Sr (1.58 Å). [51] This bondlengthening increases the size of the dipole for Ba at the surface in adirection that lowers the work function compared to Sr, and this bondstretching is likely a major reason for the work function change with Badoping. The work function reduction of 0.79 eV amounts to a surfacedipole change of approximately 0.26 eV-Å with the addition of a full Basurface layer, and can be obtained directly from VASP simulations and isalso calculable using the Helmholtz equation.[1,2]

Because Ba²⁺ is a larger cation than Sr²⁺, it was worth investigatingwhether cation segregation may occur in doped SrVO₃. As discussedpreviously, cation segregation has been observed in many perovskitematerials.[27,31-34,51-54] To ascertain if Ba segregation may occur inSrVO₃, the formation energy of substituting Ba in place of Sr wascalculated for the two cases illustrated in FIGS. 6A-6B, and alsocalculated was the segregation energy of dilute Ba (25% Ba substitutionin the middle of the surface slab) to the surface of SrVO₃. The energyto substitute Sr for Ba, ΔE_(sub), was calculated using the equationΔE_(sub)=E_(defected)−E_(perfect)−x(E_(BaO)−E_(SrO)) where E_(defected)is the total energy of the SrVO₃ surface slab with Ba substituting forSr, E_(perfect) is the energy of the undefected SrVO₃ slab, x is thenumber of Ba substitutions (in this case x=1 Ba atom in the dilutecalculation), and E_(BaO) and E_(SrO) are the total energies of rocksaltBaO and rocksalt SrO, respectively, which are taken as the referencestates for Ba and Sr atoms. It was found that the energy to substituteBa for Sr in the middle of the SrVO₃ slab (FIG. 6A) was 0.26 eV/Ba,while to substitute Ba for Sr on the surface (FIG. 6B) was −0.38 eV/Ba.The energetic driving force for Ba surface segregation is just thedifference of these energies, and is equal to −0.64 eV/Ba. Note thatwhile the value of ΔE_(sub) is, in principle, dependent on temperature,pressure, and choice of reference state, the energy difference reportedby calculating the segregation energy is the more physically insightfulquantity, and its value is independent of the chosen reference state.The magnitude of this segregation energy is consistent with DFTcalculations of cation surface segregation in other systems.[55]Therefore, if Ba is doped into SrVO₃, over time Ba will diffuse to thesurface and will dramatically lower the value of the work function.Analogous calculations for Mg and Ca doping indicate there isessentially no driving force (−0.07 eV/atom for Mg, −0.05 eV/atom forCa) to segregate these species to the SrVO₃ surface compared to the Bacase. A combined experimental and DFT study of Ca, Sr, and Ba doping in(La, Sm)MnO₃ has suggested that cation segregation is a combination ofboth elastic (via lattice strain of mismatched cation sizes) andelectrostatic effects attributed to the differing valences of alkalineearth and lanthanide elements as well as interaction with chargeddefects in doped LaMnO₃.[54] In the case of alkaline earth doping inSrVO₃ the predicted Ba cation segregation is presumably due primarily tolattice strain, as Mg, Ca, Sr and Ba are all 2+ cations and no chargeddefects or vacancies have been considered.

An important consideration of Ba doping in SrVO₃ is whether or not thesurface-segregated Ba atoms are stable on the surface. To investigatethis possibility, the adsorption energy of the Ba—O species present onthe surface was calculated relative to bulk rocksalt BaO using standardGGA-based DFT methods for three cases: ¼ monolayer Ba—O coverage onW(001) following Ref [1], ⅞ monolayer Ba—O coverage on Sc₂O₃(011)following Ref. [2], and the present case of 1 monolayer Ba—O coverage onSrVO₃ (001). These materials were chosen for comparison with SrVO₃because W(001) with BaO is the dominant emitting surface of typicalcommercial thermionic cathode devices and Sc₂O₃(011) with BaO was foundto be the most likely candidate for low work function surfaces inscandate cathode devices.[1,2] It was found that the adsorption energy(per Ba—O formula unit) for W(001), Sc₂O₃(011) and SrVO₃(001) are: 0.71eV/Ba, −0.27 eV/Ba and −1.19 eV/Ba, respectively. Since the time todesorb an atom from a material surface scales exponentially with theadsorption energy, it is evident from the above calculations that atT=1000 K, which is an approximate temperature used in thermionicemission devices, Ba will reside on the SrVO₃(001) surface approximately5 orders of magnitude longer than on Sc₂O₃(011), and approximately 9orders of magnitude longer than on W(001). Overall, thesurface-segregated Ba atoms in SrVO₃ are much more strongly bonded tothe SrVO₃ surface than the volatile Ba—O surface dipole layers presentin W- and Sc₂O₃-based electron sources. Thus, SrVO₃ can provide anelectron emission source that simultaneously exhibits an ultra-low workfunction of 1.07 eV and an operating lifetime orders of magnitude longerthan current dispenser cathode technologies.

The O 2p band center provides a way to predict the work function ofeither the AO- or BO₂-terminated surface from strictly a bulk materialsproperty. In general, surface supercell calculations are quitecomputationally expensive (especially with HSE functionals), while bulkcalculations are many times faster as a result of fewer atoms persupercell and higher supercell symmetry. Thus, the correlation betweenbulk O 2p band center and surface work function will enable fast, bulkmaterials screening of the O 2p band center to predict work functionvalues of perovskite alloys. Calculation of the bulk O 2p band center isroughly a factor of 25 times faster than calculating the work function(a factor of 50 considering both the AO- and BO₂-terminated surfaces),and thus provides a useful estimate of a perovskite work function withcomparatively minimal computational time. By high-throughput calculationof perovskite band gaps and O 2p band centers it is possible to screenfor low work function materials.[56-58] In particular, materials thatmeet the conditions of zero (or near-zero) band gap and low O 2p bandcenter will be desirable. By way of illustration, preliminaryhigh-throughput DFT screening using GGA+U has indicated that perovskiteswithin the family of (La, Pr, Y)(Ti, V)O₃ and SrVO₃ have deep O 2p bandcenters and a partially filled 3d band. Further A-site alloying ofalkaline earths and B-site alloying with other transition metals withinthis low O 2p band composition space can yield smaller (or zero) bandgapmaterials.

CONCLUSIONS

Work function values for perovskites are useful as they provide anabsolute energy band alignment of these materials versus thewell-defined vacuum reference energy level. This information isessential for applications involving electron transport at interfaces orsurfaces, including solar cells, electrocatalysts, conducting oxideelectronics, Schottky barriers, vacuum electron emitters and thermionicenergy conversion technologies. In this Example, HSE functional DFT workfunction calculations were performed for the AO- and BO₂-terminated(001) surfaces for 18 perovskite systems: the LaBO₃ materials, whereB=Sc, Ti, V, Cr, Mn, Fe, Co, Ni; the SrBO₃ materials, where B=Ti, V, Fe,Co; the La_(1-x)Sr_(x)MnO₃ materials (x=0.0625, 0.125, 0.25, 0.375),LaAlO₃ and Ba_(0.5)Sr_(0.5)Co_(0.75)Fe_(0.25)O₃ materials. The workfunction range of these materials was determined and the physics whichgoverns the value of the work function was identified and understood.Overall, the AO-terminated surfaces exhibited low work functions whileBO₂-terminated surfaces exhibited high work functions. The work functionrange of these materials was broad, and varies from as low as 1.76 eVfor AO-terminated LaMnO₃ and 1.86 eV for AO-terminated SrVO₃ to 6.87 eVfor BO₂-terminated LaAlO₃.

The O 2p band center of the bulk materials was used as an electronicstructure descriptor to develop an understanding of the work functionphysics. It was found that, in general, materials containing more 3delectrons have occupied B 3d bands that are lower in energy. As aresult, there is a larger degree of hybridization between the B 3d and O2p bands, and the position of the O 2p bands become closer to E_(Fermi).The filling of the B 3d band and subsequent increased hybridizationcauses E_(Fermi) to become deeper in energy with respect to the vacuumlevel, and the surface work function trends therefore follow those ofthe O 2p band center. We found that there is an approximately linearcorrelation between both the AO and BO₂ work functions and the value ofthe O 2p band center of the corresponding bulk materials. Interestingly,the slope of the BO₂ work function versus O 2p band center isapproximately one, indicating the change in BO₂ work function withcomposition is dominated by the shifting of the O 2p bands with respectto E_(Fermi) and hybridization as a result of 3d band filling. Thisresult demonstrates that the surface dipole for electrons leaving theBO₂ surfaces is nearly constant (within a few tenths of an eV) acrossall the systems. The nearly constant surface dipole for BO₂ surfaces canbe rationalized because the electronic states near E_(Fermi) aredominated by a mixture of B 3d and O 2p states. These electrons aredirectly present at the terminating BO₂ surface and do not have to movethrough a large additional dipole layer to emit into vacuum. On theother hand, the work function of the AO surfaces can be thought of astaking an electron from the BO₂ surface and moving it through anadditional surface dipole, which is the terminating AO surface layer.Because the AO work functions show a relatively flat trend (withinapproximately 1 eV) with B-site composition and a slope of much lessthan one with the O 2p bands, it was determined that the AO surfacedipole magnitude increases with B 3d band filling and bondhybridization. The ability to predict the value of a surface quantitysuch as the work function from just a bulk materials property like the O2p band center provides the opportunity for fast, high-throughputscreening of perovskite compounds for materials with desired magnitudeof work function.

Electron-emission cathode materials find application in high powerelectron beam devices used in defense, scientific research andcommunications applications and in thermionic energy conversiontechnologies. Electron emitters suitable as an electron source desirablyexhibit a low work function, stability in conditions of high temperatureand low pressure, and sufficient conductivity to sustain the desiredemission current. As compared to scandate and other thermionic cathodes,perovskites possess natively polar surfaces; as such, an additionalvolatile adsorbed dipole layer is not necessary to realize a low workfunction. SrVO₃ was found to meet the above criteria, exhibiting one ofthe lowest calculated work function of the materials considered here,equal to 1.86 eV for the AO-terminated (001) surface. Additional workfunction calculations for (011)-oriented surfaces terminated by both Oand ABO surfaces and (111)-oriented surfaces terminated by both B andAO₃ surfaces were performed. It was found that these surfaces allpossessed higher work functions than the AO-terminated (001) surfaces.However, the (001)-oriented SrVO₃ surfaces were the most stable of thoseconsidered. On thermodynamic grounds, low work function (001)-surfacesshould dominate in quantity over other surface terminations in realdevices.

The last portion of the investigation of SrVO₃ involved Ba doping tofurther lower the work function. By comparing the effect of doping Bainto the middle of the surface slab versus in the terminating surfacelayer, it was found that while doping Ba into the middle of the slabbarely raised the AO-terminated work function to 1.90 eV, doping Ba intothe top surface layer resulted in a very low work function of only 1.07eV. In addition, it was discovered that there was a tendency of Ba tosegregate to the surface of SrVO₃, with a segregation energy of −0.64eV/Ba. The Ba cation segregation is presumably the result of the largerBa²⁺ cation creating a lattice strain which is relieved by having Baoccupy the surface rather than bulk lattice sites. Lastly, it wasdetermined that the Ba adsorption energy of Ba—O on SrVO₃ was morestable than Ba—O adsorption on W(001) and Sc₂O₃(011) surfaces,indicating that Ba will reside on the SrVO₃ surface orders of magnitudelonger than on other widely explored thermionic cathode materialsurfaces.

Example 2

In this example, the methods described in Example 1, above, were used toanalyze the transition metal perovskite oxide BaNbO₃. The work functionof this material was found to be 1.5 eV.

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The word “illustrative” is used herein to mean serving as an example,instance, or illustration. Any aspect or design described herein as“illustrative” is not necessarily to be construed as preferred oradvantageous over other aspects or designs. Further, for the purposes ofthis disclosure and unless otherwise specified, “a” or “an” means “oneor more”.

The foregoing description of illustrative embodiments of the inventionhas been presented for purposes of illustration and of description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed, and modifications and variations are possible inlight of the above teachings or may be acquired from practice of theinvention. The embodiments were chosen and described in order to explainthe principles of the invention and as practical applications of theinvention to enable one skilled in the art to utilize the invention invarious embodiments and with various modifications as suited to theparticular use contemplated. It is intended that the scope of theinvention be defined by the claims appended hereto and theirequivalents.

What is claimed is:
 1. An electron emitter device comprising: a cathodecomprising a conductive transition metal perovskite oxide comprisingmobile conducting electrons exhibiting a conductivity of at least 10⁻⁶Ω⁻¹-cm⁻¹ at room temperature, the transition metal perovskite oxidehaving a surface from which the mobile electrons are induced to emitupon receiving sufficient energy from an energy source; and an anodeelectrically coupled to the cathode and positioned to define aninterelectrode conductive region between the anode and the cathode, ontowhich anode the emitted electrons are collected, wherein the transitionmetal perovskite oxide does not have the formula (La,Ba,Sr)TiO₃.
 2. Theelectron emitter device of claim 1, further comprising an enclosureconfigured to enclose the cathode, the anode and the interelectrodeconductive region.
 3. The electron emitter device of claim 2, whereinthe enclosed space provided by the enclosure is evacuated to a vacuum.4. The electron emitter device of claim 1, wherein the transition metalperovskite oxide has the formula ABO₃, wherein A is selected from analkaline earth element, a rare earth element, and combinations thereofand B is selected from a 3d transition metal element, a 4d transitionmetal element, and combinations thereof.
 5. The electron emitter deviceof claim 4, wherein A is selected from Mg, Ca, Sr, Ba, La, Pr, Sc, Y,and combinations thereof and B is selected from Sc, Ti, V, Cr, Mn, Fe,Co, Ni, Nb, and combinations thereof.
 6. The electron emitter device ofclaim 4, wherein A is selected from Mg, Ca, Sr, Ba, La, Pr, Y and B isselected from Ti, V, Mn, Fe, Nb, and combinations thereof.
 7. Theelectron emitter device of claim 1, wherein the transition metalperovskite oxide has formula AVO₃, wherein A is selected from analkaline earth element, a rare earth element, and combinations thereof.8. The electron emitter of claim 7, wherein the transition metalperovskite oxide has formula (A₁)_(1-x)(A₂)_(x)VO₃, wherein A₁ and A₂are independently selected from an alkaline earth element and a rareearth element, wherein 0≤x≤1.
 9. The electron emitter device of claim 8,wherein A₁ and A₂ are independently selected from Mg, Ca, Sr, Ba, La,Sc, and Y.
 10. The electron emitter device of claim 1, wherein thetransition metal perovskite oxide is selected from formulaSr_(1-x)Ba_(x)VO₃, formula La_(1-x)Sr_(x)MnO₃, LaFeO₃, and BaNbO₃,wherein 0≤x≤1.
 11. The electron emitter device of claim 1, wherein thetransition metal perovskite has formula Sr_(1-x)Ba_(x)VO₃, wherein0≤x≤1.
 12. The electron emitter device of claim 1, wherein thetransition metal perovskite oxide exhibits a calculated work function ofless than about 2.50 eV.
 13. The electron emitter device of claim 1,wherein the mobile conducting electrons exhibit a conductivity of atleast 10⁻² Ω⁻¹cm⁻¹ at room temperature.
 14. The electron emitter deviceof claim 1, wherein the transition metal perovskite oxide exhibits ameasured band gap of no more than about 2 eV.
 15. The electron emitterdevice of claim 1, wherein the transition metal perovskite oxide ischaracterized by an O 2p-band center and E_(Fermi) and the calculatedenergy difference Δ between the O 2p-band center and E_(Fermi) is −3 eVor more.
 16. The electron emitter device of claim 1, wherein asufficient fraction of the surface of the transition metal perovskiteoxide has (001) orientation and AO-termination such that the surfaceexhibits an effective work function which is substantially similar tothe work function of a surface which is substantially (001) orientatedand substantially AO-terminated.
 17. The electron emitter device ofclaim 1, wherein the cathode is formed entirely of the transition metalperovskite oxide.
 18. A source of microwaves or millimeter wavescomprising the electron emitter device of claim
 1. 19. A thermionicenergy converter comprising the electron emitter device of claim 1.